Question

calculate the average atomic mass for this element. isotope - mass | percent abundance x-84 | 0.56 x-86 | 9.86 x-87 | 7.00 x-88 | 82.58

Explanation:

Step1: Recall the formula for average atomic mass

The formula for average atomic mass ($A$) is the sum of the product of each isotope's mass ($m_i$) and its percent abundance ($p_i$) (converted to a decimal) for all isotopes. Mathematically, $A=\sum (m_i\times\frac{p_i}{100})$.

Step2: Calculate the contribution of each isotope

• For X - 84: Mass $m_1 = 84$, Percent abundance $p_1=0.56$. Contribution: $84\times\frac{0.56}{100}=84\times0.0056 = 0.4704$
• For X - 86: Mass $m_2 = 86$, Percent abundance $p_2 = 9.86$. Contribution: $86\times\frac{9.86}{100}=86\times0.0986=8.4796$
• For X - 87: Mass $m_3 = 87$, Percent abundance $p_3 = 7.00$. Contribution: $87\times\frac{7.00}{100}=87\times0.07 = 6.09$
• For X - 88: Mass $m_4 = 88$, Percent abundance $p_4 = 82.58$. Contribution: $88\times\frac{82.58}{100}=88\times0.8258 = 72.6704$

Step3: Sum up all the contributions

Add the contributions from each isotope: $0.4704 + 8.4796+6.09 + 72.6704$.
First, $0.4704+8.4796 = 8.95$; then $8.95 + 6.09=15.04$; then $15.04+72.6704 = 87.7104$

Answer:

The average atomic mass of the element is approximately $87.71$ (units are atomic mass units, usually).